Fixed Income Level 2

Answer B In order to find the price you need to use the forward bond pricing model but first you need to find the price of the a 3 year bond thus: 1/(1.0226)^3=.93515 Price of 6 year bond= Price of 3 year bond * Forward price of 3 years starting in 3 years. .85575=.93515*.9151 Or you can do the other way around and find the rate of the 3 year forward bond in 3 years from now and multiply by the 3 year spot rate that is given to find the rate of the 6 year bond. Using the rate of the 6 year bond you can convert to the price. 1/(1+R3)^3=.9151 thus R=.03001563 (1+Rate of 6 year)^6=(1.0226)(1.3001563) Price of 6 year bond= 1/(1+R6)^6 thus (1/1.68554064)=.8558

(2) 1 year spot: 1.50% 2 year spot: 2.005% 3 year spot: 2.26% If the three year forward price of a three year zero coupon bond is $0.9151 (per $1 par), the price today of a six year zero coupon bond should be closest to? A) .07899 B) .8558 C) .9311

(0) Path Year 1 Year 2 Year 3 1 2% 2.8050% 4.0787% 2 2% 2.8050% 3.0216% 3 2% 2.0780% 3.0216% 4 2% 2.0780% 2.2384% Dixon wants Song to value three-year, 4% annual pay, $100 face value Zena, Inc., bonds. The bonds have a Bermudan-style call option that can be exercised at par in one and two years. Comparable bonds have an OAS of 100bps. Dixon explains to Song that investments in callable bonds have special interest rate risk considerations. Using the information given in the case and in Figure 1, the value of 4% Zena, Inc., callable bond is closest to: A)$97.12 B)$100.00 C)$100.82

1) build out tree 2)Add the 100bps to each interest rate 3) Calculate the nodes. 4) For a callable bond, replace the call price $100 if the value is higher for the node on year 2. Since company will call back bond.

(1) How to find present value of a semi annual bond Example 1: Calculate the price of a bond with a par value of $1,000 to be paid in ten years, a coupon rate of 10%, and a required yield of 12%. In our example we'll assume that coupon payments are made semi-annually to bond holders and that the next coupon payment is expected in six months. Here are the steps we have to take to calculate the price:

1. Determine the Number of Coupon Payments: Because two coupon payments will be made each year for ten years, we will have a total of 20 coupon payments. 2. Determine the Value of Each Coupon Payment: Because the coupon payments are semi-annual, divide the coupon rate in half. The coupon rate is the percentage off the bond's par value. As a result, each semi-annual coupon payment will be $50 ($1,000 X 0.05). 3. Determine the Semi-Annual Yield: Like the coupon rate, the required yield of 12% must be divided by two because the number of periods used in the calculation has doubled. If we left the required yield at 12%, our bond price would be very low and inaccurate. Therefore, the required semi-annual yield is 6% (0.12/2). PV=1000 N=10*2=20 I/Y= 12%/2=6% PMT=(1000*10)/2=50 Calculate PV=885.3 Remember if semiannual then multiply number of payments, divide interest rate, divide payments.

(2) With respect to local expectations theory, which of the following statements is most consistent with market evidence? A)Short-term holding period return of long-maturity bonds exceeds the short-term holding period returns of short-maturity bonds. B)Short-term holding period return of long-maturity bonds and the short-term holding period return of short-maturity bonds is the same. C)Short-term holding period return of short-maturity bonds exceeds the short-term holding period returns of long-maturity bonds.

Answer A Market evidence shows that short-term holding period returns from investing in long-maturity bonds exceed the short-term holding period returns from investing in short-maturity bonds.

(1) Which of the following statements regarding evaluating credit risk of Asset Backed Securities (ABS) is least accurate? A)Unlike for corporate debt, structural and reduced form models are not appropriate. B)The analysis should entail consideration of the composition of the collateral pool and the cash flow waterfall. C)Credit rating agencies use the same credit ratings for ABS as for corporate debt.

Answer A Reduced form and structural models can be used as long as they take into account the complex structure of the ABS.

(1) An investor currently holds a zero coupon bond that matures in two years and has a face value of $100,000. The continuously compounded risk free rate is 0.60% and the bond issuer's credit spread is 0.25%. The present value of the expected loss implied by the credit spread is closest to: A)$493. B)$246. C)$1,679.

Answer A

(2) Using the following interest rate tree of semiannual interest rates what is the value of an option free semiannual bond that has one year remaining to maturity and has a 6% coupon rate? UP 6.53% Original 6.30% Down5.67% A)99.81. B)97.53. C)98.52.

Answer A Since this is semiannual pay bond divide interest rates by half and the coupon payment by half thus: .5(100+3)+.5(100+3)/1.03265=99.74 .5(100+3)+.5(100+3)/1.02835=100.16 (.5(99.74+3)+.5(100.16+3))/1.0315=99.81

(2) Thompson states, reduced form models perform better than structural models as they tend to impose assumptions on the outputs of the structural model. However reduced form models require specification of company balance sheet composition Thompsons statement about reduced form models relative to structural model is most likely A)Correct B) Incorrect regarding assumptions imposed C)incorrect regarding specification of balance sheet composition required?

C.

(1) For longer-term financing, Acton wants to investigate issuing a convertible bond. Foster has suggested a 10-year convertible bond with a 3.5% annual coupon that would be convertible at the rate of 45 Acton shares per $1,000 par bond. Acton shares are currently trading at $20 and have an expected dividend yield of 2.8% for the coming year. Foster states that the conversion feature would lower the yield on the bond from 3.5% to 3%. The market conversion premium ratio on the convertible bond is closest to: A)0.5%. B)9.8%. C)15.85%.

Value of convertible: PMT = 35, N = 10, I/Y = 3, FV = 1,000; CPT PV = 1,042.65 Straight value = 1,000 (coupon rate = yield) Market conversion price = price of convertible / conversion ratio = 1,042.65/45=23.17 Market conversion premium per share = market conversion price - stock's market price = 23.17 - 20=$3.17 Market conversion premium ratio=market conversion premium per share/stock price = 3.17/20=15.85%

(3) T/F Credit ratings are volatile over time which reduces their usefulness as an indication of a debt offerings default probability Ratings do not implicitly depend on the business cycle stage, whereas a debt offering's default probability does

False and True Credit ratings are stable over time which reduces their usefulness as an indication of a debt offerings default probability

(2) What are three assumptions of using YTM? and what happens if these are violated?

If the spot rate curve is upward sloping then the YTM will be lower than the actual realized return. The realized return would be greater than the yield to maturity "YTM" because the coupons would be reinvested at forward rates which increase and eventually exceed the YTM since the spot curve is upward sloping. The YTM can be a poor estimate of expected return if interest rates are volatile and if the yield curve is steeply sloped (up or down).

What are the three conditions required for multi liability immunization?

) PV A = PV L 2) Composite duration of the portfolio must = composite duration of the liabilities 3) Individual portfolio assets must have at least one asset duration less than the lowest liability duration and at least one asset with a duration higher than the longest liability duration, ie: have a wider range. Suppose that you have a liability due is 2 years. You want to invest in a bond with 2 years or less to maturity (so that you have cash to pay the liability), but its duration will likely be too short for classical immunization. So you also have to have a bond whose maturity is longer than 2 years so that the duration of the portfolio matches that of the liability. One longer, one shorter.

Flip Flip Flip VU=.5(105+105)/1.059=99.52 VL=.5(105+105)/1.059=100.28965 Present= ((99.52+100.28965+10)/2)/1.052=99.72 To value the 2-year note with no embedded options, we simply average the present values of the two possible values from the next period. From this value, the yield to maturity at issuance can then be calculated using our financial calculator: PV = −99.72, N = 2, PMT = 50, FV = 1,00 CPT I/Y = 5.15% Since the note is putable at par ($100) after one year, the put option will be exercised at the upper year-one node since the value is less than $100. If the value is less than $100 and you have a put par then you can sell at par which is $100. So, the bond value at this node is replaced by $1,00 (plus the $5 coupon). VU=.5(105+105)/1.059=99.52 but lower than par thus you would sell at $100 with your par put VL=.5(105+105)/1.059=100.28965 Present= ((100+100.28965+10)/2)/1.052=99.94

Alan Foster, CFA, is a fixed income analyst for Quantshop, an investment management firm. Alan has been asked by his supervisor to prepare an analysis of a proposed bond offering by Acton Industries. The proposed offering is a 2-year annual-pay bond with a 5% coupon which Quantshop management believes will carry a single A rating. As part of his analysis, Foster has been asked by Acton to consider the effect on the market yield of options that may be embedded in the note offering, specifically a par call after one year or a par put after one year. If Acton issues the 2-year note with no embedded options, the yield to maturity at issuance will be closest to: A)5.15%. B)5.20%. C)5.25%. The issue price of the note issue (% of par) if Acton chooses to issue the putable note is closest to: A)99.895. B)99.946. C)100.27.

(1) Berg also observes that the current Treasury bond yield curve is upward sloping. Based on this observation, Berg forecasts that short-term interest rates will increase. Is Berg's short-term interest rate forecast consistent with the pure expectations theory and the liquidity premium theory? A)Consistent with both theories. B)Consistent with the liquidity premium theory only. C)Consistent with the pure expectations theory only.

An upward sloping yield curve predicts an increase in short-term rates according to the pure expectations theory but not necessarily the liquidity premium theory. Short term interest rates may stay flat but the liquidity premium theory makes the curve upward sloping due to liquidity premiums for longer dated bonds. Therefore, just because the curve is upwards sloping doesn't mean the short term rates will rise according to the liquidity premium theory. The liquidity theory says that forward rates are a biased estimate of the market's expectation of future rates because they include a liquidity premium. Therefore, a positive sloping yield curve may indicate either (1) that the market expects future interest rates to rise or (2) that rates are expected to remain constant (or even fall), but the addition of the liquidity premium results in a positive slope.

(1) After reviewing Diffle's analysis, Puldo notes that Diffle has not included any information on the option adjusted spread (OAS) for the Hardin bonds. Puldo suggests that Diffle should evaluate the OAS in order to get an idea of the liquidity risk of the Hardin bonds. Diffle counters that the OAS may not be very informative in this case, since he is uncertain as to the reliability of the interest rate volatility assumption. Which of the following most accurately critiques the OAS discussion between Diffle and Puldo? Puldo is: A)correct that the OAS will provide insight into the liquidity risk of the Hardin bonds, and Diffle is correct that different volatility assumptions would change the OAS. B)incorrect that the OAS will provide insight into the liquidity risk of the Hardin Bonds, but Diffle is correct that different volatility assumptions would change the OAS. C)correct that the OAS will provide insight into the liquidity risk of the Hardin Bonds, but Diffle is incorrect since OAS implicitly adjusts for the volatility of interest rates.

Answer A The OAS accounts for compensation for credit and liquidity risk after the optionality has been removed (i.e., after cash flows have been adjusted). Since in this case the credit risk of the bonds is similar, the OAS could prove helpful in evaluating the relative liquidity risk. OAS will be affected by different assumptions regarding the volatility of interest rates. Binomial trees generated under an assumption of high volatility will lead to higher values for a call option and a corresponding lower value for a callable bond. Under a high volatility assumption, we would already have a lower computed value for the callable bond, and hence, the additional spread (i.e., the OAS) needed to force the discounted value to equal the market price will be lower. When an analyst uses a lower-than-actual (higher-than-actual) level of volatility, the computed OAS for a callable bond will be too high (low) and the bond will be erroneously classified as underpriced (overpriced). Similarly, when the analyst uses a lower-than-actual (higher-than-actual) level of volatility, the computed OAS for a putable bond will be too low (high) and the bond will be erroneously classified as overpriced (underpriced).

The forward contract price of a bond is most likely to decrease if spot rates in the future: A) turn out to be higher than the corresponding current forward rates. B) turn out to be lower than the corresponding current forward rates. C) evolve according to the forward curve.

Answer A The forward contract price of a bond and current spot rates move inversely to rates. A forward contract price is just a contract to buy a bond at a future price. Thus if interest rates are above current forward rates then the price of the bond and the forward contract price will drop. The forward contract price of a bond is inversely related to evolution of spot rates. If the future spot rates evolve to be the same as the current forward rates, the forward price will be unchanged. However, if the future spot rates are higher (lower) than the current forward rates, the forward price will decrease (increase).

(2) If the liquidity preference hypothesis is true, what shape should the term structure curve have in a period where interest rates are expected to be constant? A)Upward sweeping. B)Downward sweeping. C)Flat.

Answer A The liquidity theory holds that investors demand a premium to compensate them for interest rate exposure and the premium increases with maturity. Add this premium to a flat curve and the result is an upward sloping yield curve.

(3) A portfolio manager who believed in the liquidity premium theory would expect: A)long-term rates to be higher than investors' expectations of future rates, because of the liquidity premium. B)long-term securities to offer higher returns than short-term securities. C)short-term rates to be lower than investors' expectations of short-term rates, because of the liquidity premium.

Answer A The liquidity theory of the term structure proposes that forward rates reflect investors' expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk, and this liquidity premium is positively related to maturity. The implication of the liquidity theory is that forward rates, since they include a liquidity premium, are a biased estimate of the market's expectation of future spot rates. It's not answer B because the curve could be inverted. In that case, the liquidity premium would increase the long term return but may not increase enough to offset a higher short term rate. It's not Answer C because the liquidity premium is always either 0 or Greater. Thus it would never lower your required return, if anything it would increase.

(2) What is the market conversion price of a convertible security? A)The price that an investor pays for the common stock if the convertible bond is purchased and then converted into the stock. B)The value of the security if it is converted immediately. C)The price that an investor pays for the common stock in the market.

Answer A The market conversion price, or conversion parity price, is the price that the convertible bondholder would effectively pay for the stock if she bought the bond and immediately converted it. market conversion price = market price of convertible bond ÷ conversion ratio.

(2) According to the pure expectations theory, which of the following statements is most accurate? Forward rates: A)exclusively represent expected future spot rates. B)always overestimate future spot rates. C)are biased estimates of market expectations.

Answer A The pure expectations theory, also referred to as the unbiased expectations theory, purports that forward rates are solely a function of expected future spot rates. Under the pure expectations theory, a yield curve that is upward (downward) sloping, means that short-term rates are expected to rise (fall). A flat yield curve implies that the market expects short-term rates to remain constant.

(2) Suppose the government spot rate curve is flat at 3%. An active manager is planning on purchasing a five-year government bond at par. The realized return on this bond will most likely be: A)3% if the bond is held to maturity provided that the yield curve remains flat at 3%. B)more than 3% if the bond is held to maturity while the yield curve remains flat but decreases below 3%. C)3% if the bond is held to maturity regardless of the shape of the yield curve.

Answer A There is no price risk for a default-free bond held to maturity. However, there is reinvestment risk for the coupon payments received during the life of the bond (in this instance, the bond is a par bond and hence has the same coupon rate as its yield). If the yield curve shifts down, the reinvestment rate would be lower and the realized holding period return would be lower than 3%.

(.5) The price of a five-year zero coupon bond is $0.7835 for $1 par and the price of a two-year zero-coupon bond is $0.9426 for $1 par. The three-year forward rate two years from now is closest to: A)6.36% B)5.54% C)4.87%

Answer A You are trying to find Forward Rate but first you need to find the forward price using forward pricing model. .7835=.9426*($F) F=.831211 To go from Forward Price to Forward Rate FP=Par Value/(1+FR)^n-m .831211= $1/(1+X)^3 X=.06356

(1) Credit risk in the banking system is most accurately captured by the: A)10-year swap spread. B)TED spread. C)I-spread.

Answer B Comparing the TED spread with the 10-year swap spread, the TED spread more accurately reflects the risk in the banking system, while the 10-year swap spread mostly reflects differing supply and demand conditions. An I-spread refers to a bond yield net of the swap rate of the same maturity.

(3) How do the risk-return characteristics of a newly issued convertible bond compare with the risk-return characteristics of ownership of the underlying common stock? The convertible bond has: A)lower risk and lower return potential. B)lower risk and higher return potential. C)higher risk and higher return potential.

Answer A Buying convertible bonds in lieu of direct stock investing limits downside risk due to the price floor set by the straight bond value. The cost of the risk protection is the reduced upside potential due to the conversion premium.

(1) Which bonds would have its maturity-matched rate as its most critical rate? A)Low coupon callable bonds. B)High coupon callable bonds. C)Low coupon putable bonds.

Answer A Callable bonds with low coupon rate are unlikely to be called; hence, their maturity-matched rate is their most critical rate (i.e., the highest key rate duration corresponds to the bond's maturity). Similarly, putable bonds with high coupon rates are unlikely to be put and are most sensitive to their maturity-matched rates.

(3) A corporate bond has one year to maturity with a probability of default of 2.05% and a recovery rate of $32.00 per $100 par value. If an investor holds $100,000 of par value, what is the expected loss? A)$1,394. B)$2,050. C)$656.

Answer A Expected loss = Probability of default × expected loss per $ × par value = 0.0205 × (1 − 0.32) × $100,000 = $1,394

(2) Which of the following is a correct statement concerning the backward induction technique used within the binomial interest rate tree framework? From the maturity date of a bond: A)the corresponding interest rates and interest rate probabilities are used to discount the value of the bond. B)the corresponding interest rates are weighted by the bond's duration to discount the value of the bond. C)a deterministic interest rate path is used to discount the value of the bond.

Answer A For a bond that has N compounding periods, the current value of the bond is determined by computing the bond's possible values at period N and working "backwards" to the present. The value at any given node is the probability-weighted average of the discounted values of the next period's nodal values. The probability is really just 50/50.

(1) For a convertible bond without any other options, the call feature implied by the convertibility feature will do all of the following EXCEPT: A)cause negative convexity. B)increase the value of the bond over that of a comparable option-free bond. C)place a lower limit on the possible values of the bond.

Answer A Negative convexity is caused by the bond being callable where the issuer has the embedded call option. Negative convexity does not apply to convertible bonds since the call option for stock is in your favor so its not the same thing. The convertibility feature gives the bondholder a call option on the shares of common stock of the issuer. This increases the price of the bond and places a lower limit on the possible values of the bond. However, that lower limit will change with the price of the common stock.

(2) Gill Westmore is the fixed income portfolio manager for Allied Insurance. Westmore has bought protection using a 2-year CDS on CDX-IG (125 constituent) index. The notional is $200 million. Company X, an index constituent defaults and trades at 25% of par. The payoff on the CDS on account of default of X and the notional principal of the CDS after default are closest to: Payoff Notional A)$1.2 million $198.4 million B)$1.5 million $198 million C)$1.6 million $200 million

Answer A Notional principal attributable to bonds of company X = $200 million/125 = $1.6 million. Payoff on the CDS = $1.6 million − (0.25)($1.6 million) = $1.2 million. After default, the CDS continues with (200-1.6) $198.4 million of notional principal.

(1) During the discussions, Rogers makes the following statements: Statement 1: If the volatility of interest rates decreases, the value of the callable bond will increase. Statement 2: The noncallable bond will not be affected by a change in the volatility or level of interest rates. Statement 3: When interest rates decrease, the value of the noncallable bond increases by more than the callable bond. Statement 4: If the volatility of interest rates increases, the value of the putable bond will increase. Evaluate Rogers's statements 1 and 3. A)Both statements are correct. B)Only Statement 3 is correct. C)Only Statement 1 is correct.

Answer A Statement 1 is correct. If the volatility of interest rates decreases, the call option is less valuable, which increases the value of the callable bond. Recall that Vcallable = Vnoncallable − Vcall. Statement 3 is also correct. The value of the noncallable bond increases by more than the callable bond because as yield falls, the value of the call goes up. As the call value increases, the callable value (noncall value − call option value) goes up by less than the noncall value.

(2) During the discussions, Rogers makes the following statements: Statement 1: If the volatility of interest rates decreases, the value of the callable bond will increase. Statement 2: The noncallable bond will not be affected by a change in the volatility or level of interest rates. Statement 3: When interest rates decrease, the value of the noncallable bond increases by more than the callable bond. Statement 4: If the volatility of interest rates increases, the value of the putable bond will increase. Evaluate Rogers's statements 2 and 4. A)Only Statement 4 is correct. B)Only Statement 2 is correct. C)Both statements are correct.

Answer A Statement 2 is incorrect because the noncallable bond value will be affected by a change in the level of interest rates. Statement 4 is correct because higher interest rate volatility will increase the value of the embedded put option and increase the value of the puttable bond.

(2) For an interest rate swap, the swap spread is the difference between the: A)swap rate and the corresponding Treasury rate. B)fixed rate and the floating rate in a given period. C)average fixed rate and the average floating rate over the life of the contract.

Answer A The swap spread is the swap rate minus the corresponding Treasury rate.A swap spread is the difference between the fixed rate on an interest rate swap and a Treasury bond of maturity equal to that of the swap. Investors use the swap spread to separate the time value portion of a bond's yield from the risk premia for credit and liquidity risk. The higher the swap spread, the higher the compensation for liquidity and credit risk.

(3) Wall wonders how the value of the callable bond changes when interest rate volatility increases. How will an increase in volatility affect the value of the callable bond? The value: A)decreases. B)increases. C)may increase or decrease.

Answer A The value of the callable bond decreases if the interest rate volatility inreases because the value of the embedded call option increases. Since the value of the callable bond is the difference between the value of the non-callable bond and the value of the embedded call option, its value has to decrease. In other words, volatility increases the value of the call option which decreases the value of the call bond.

(1) The active bond portfolio management strategy of rolling down the yield curve is most consistent with: A)liquidity preference theory. B)segmented markets theory. C)pure expectations theory.

Answer A Under the liquidity preference theory, investors would earn an extra return for investing in longer-maturity bonds rather than in shorter-maturity bonds. Such extra positive risk-premium linked to maturity of the bonds is absent in the pure expectations and the market segmentation theory. When the yield curve is upward sloping, bond managers may use the strategy of "riding the yield curve" to chase above-market returns. By holding long-maturity rather than short-maturity bonds, the manager earns an excess return as the bond "rolls down the yield curve" (i.e., approaches maturity and increases in price). As long as the yield curve remains upward sloping, this strategy will add to the return of a bond portfolio. Basically if you get a long maturity bond you will get a higher coupon rate of say 6% (i.e. $60 each year on a $1,000 par bond) but as it gets closer to maturity your discount rate lessens.

(1) 5-year, 5% Zillon Corp. bonds currently trade at $980 reflecting credit spread of 3%. A 5-year CDS for Zillon bonds has a coupon rate of 5%. The duration of the CDS = 4. The upfront payment made/received by the protection buyer on a $4 million notional CDS is closest to: A)$320,000 received by the protection buyer. B)$400,000 received by the protection buyer. C)$300,000 paid by the protection buyer.

Answer A Upfront payment = (CDS spread − CDS coupon) × duration × notional principal = (0.03 − 0.05) × 4 × 4,000,000 = −$320,000 The protection buyer will receive an upfront premium of $320,000.

(1) Wabush is not convinced that the central bank will follow through on their commitment to keep rates constant. He has heard rumors that the bank will announce next month that the policy will be reviewed, with the potential for almost immediate changes in target rates. Wabush is concerned that this will introduce significant volatility into the term structure of interest rates. If the rumors Wabush has heard regarding the central bank announcement are true, the uncertainty would most likely increase volatility: A)in short-term rates more than in long-term rates. B)in long-term rates more than in short-term rates. C)equally in long-term and short-term rates.

Answer A Volatility at the long-maturity end is thought to be associated with uncertainty regarding the real economy and inflation, while volatility at the short-maturity end reflects risks regarding monetary policy.

(2) Joseph Dentice, CFA is evaluating three bonds. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable at any time at par and bond C is putable at any time at par. Yield curve is currently flat at 3%. The bond least likely to have the highest one-sided down-duration is: A)Bond B. B)Bond C. C)Bond A.

Answer A When the underlying option is at (or near) money, callable bonds will have lower one-sided down-duration than one-sided up-duration; the price change of a callable when rates fall is smaller than the price change for an equal increase in rates. When the underlying option is at (or near) the money, callable (putable) bonds will have lower (higher) one-sided down-duration than onesided up-duration.

(2) Joseph Dentice, CFA is evaluating three bonds. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. If interest rates increase, the duration of which bond is most likely to decrease? A)Bond C. B)Bond B. C)Bond A.

Answer A (bond C) Increase in rates would increase the likelihood of the put option being exercised and reduce the expected life (and duration) of the putable bond the most.

(-1) The following are some of the current par rates: Year Par rate 1 5.00% 2 6.00% 3 7.00% Using bootstrapping, the 3-year spot rate is closest to: A)7.09% B)6.93% C)6.67%

Answer A. Par rates are the rates that you could discount each of your cash flows so that the PV of the bond equals the Par Value. For example in year 2 the par value is the discount rate you can use so that $6/(1+X)+(100+6)/(1+X)^2=$100 Par Rates can be used to find spot rates via bootstrapping. (100*Par%2)/(1+Par%1) +100(Par%2)+100/(1+X)^2=100 solve for X Then (100*Par%3)/(1+Par%1) +(100(Par%3))/(1+S2)^2+((100*Par%3)+100)/(1+X)^3=100 solve for X

(2) Bill Moxley, CFA is evaluating three bonds for inclusion in fixed income portfolio for one of his pension fund clients. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. The yield curve is currently flat. If the yield curve becomes upward sloping, the bond least likely to have the highest price impact would be: A)Bond C B)Bond A C)Bond B

Answer A: Bond C Bond C is putable and hence has limited downside potential when rates rise. The other two bonds do not have any such protection.

(1) Don McGuire, fixed income specialist at MCB bank makes the following statement: "In the very short-term, the expected rate of return from investing in any bond, including risky bonds, is the risk-free rate of return". McGuire's statement is most consistent with: A)unbiased expectations theory. B)local expectations theory. C)liquidity preference theory.

Answer B *Local expectations theory asserts that in the very short term, the expected return for every bond is the risk-free rate* but does not extend the risk-neutrality assumption to every maturity strategy like the unbiased expectations theory.

(2) Which of the following strategies would be most appropriate use of CDS given an expectation of credit curve steepening? A)Engage in a naked CDS. B)A curve steepening trade. C)A curve flattening trade.

Answer B A credit curve steepening expectation would entail the credit spread for longer maturities increasing relative to the change in credit spread for shorter maturities. In such a scenario, one would buy protection for longer maturities and sell protection for shorter maturity (i.e., a curve steepening trade).

(2) Wall now turns his attention to the value of the embedded call option. How does the value of the embedded call option react to an increase in interest rates? The value of the embedded call to the issuer of the bond is most likely to: A)remain the same. B)decrease. C)increase.

Answer B Callable bonds allow the bond issuer (i.e. the company) to buy back bonds if interest rates drop past a certain point so they can reissue bonds at a lower price. Thus when interest rates rise the value of the call decreases.

(2) "Choosing to invest in MediSoft's convertible bond would benefit our portfolios in many ways, but the primary benefit is the limited downside risk associated with the bond. Because the straight value will provide a floor for the value of the convertible bond, downside risk is limited to the difference between the market price of the bond and the straight value." Under what circumstances will the analyst's comments regarding the limited downside risk of MediSoft's convertible bonds be accurate? A)The convertible bond is trading in the market as a common stock equivalent. B)Short-term and long-term interest rates are expected to remain the same. C)The Federal Reserve Bank decides to pursue a restrictive monetary policy.

Answer B Convertible Bond Market Value= Straight Value of Bond + Option Value If rates stay the same then the straight value will remain the same. The worst that can happen is that the option value goes to zero. If interest rates are not expected to change then the straight value of the bond will not change (ignoring the change in value resulting from the passage of time). If the straight value does not change, then downside risk is indeed limited to the difference between the price paid for the bond and the straight value. If, however, interest rates rise as the price of the common stock falls, the conversion value will fall and the straight value will fall, exposing the holder of the convertible bond to more downside risk.

(1) What adjustment must be made to the key rate durations to measure the risk of a steepening of an already upward sloping yield curve? A)Increase the key rates at the short end of the yield curve. B)Decrease the key rates at the short end of the yield curve. C)Increase all key rates by the same amount.

Answer B Decreasing the key rates at the short end of the yield curve makes an upward sloping yield curve steeper. Performing the corresponding change in portfolio value will determine the risk of a steepening yield curve.

(3) Which of the following statements regarding using a reduced form model to assess credit risk is least accurate? A)Under the assumption of no arbitrage, the price of debt is equal to the expected discounted payoff at maturity. B)The model assumes that the company's assets trade in frictionless markets. C)The company has debt that trades in frictionless markets.

Answer B Reduced form models do not require a company's assets to trade in frictionless markets

(0) A 2-year $1,000 par, 5% (semi-annual pay) Mexa-corp bond has a Z-spread of 45bps. Using the following spot curve, compute the invoice price of the bond. Maturity 0.50 1.00 1.50 2.00 Spot rates 4.50% 5% 5.25% 5.5% A)$993.45 B)$982.65 C)$956.32

Answer B The Z-spread is the spread that when added to each spot rate on the yield curve makes the present value of a bond's cash flows equal to the bond's market price Nominal spread is the difference in YTM between the risky bond and a risk-free bond (usually a Treasury) of the same maturity; it is a spread added to one point on the Treasury par curve. Thus, the nominal spread ignores the term structure of interest rates; it uses only one point, not the entire yield curve. The Z-spread is added to every point on the (zero-volatility) spot curve; it uses the entire yield curve, not just one point. The OAS is added to every point on the (nonzero-volatility) spot curve; it uses the entire yield curve, not just one point. The difference between the Z-spread and the OAS is that the Z-spread includes the spread for any embedded options (along with the spread for all other risks associated with the bond), whereas the OAS removes the spread for the embedded options, leaving only the spread for all other risks associated with the bond. The Z-spread minus the OAS is the price of the empedded option(s), measured in bp of return (instead of being measured in price difference).

(2) Which of the following two securities are most likely used to calculate the term structure of credit spreads? A)A corporate issuer's coupon paying bond and the same issuer's zero coupon bond. B)A corporate issuer's zero coupon bond and a default free zero coupon bond. C)A corporate issuer's senior debt and the same issuer's subordinated debt.

Answer B This question essentially asks what are the components of spread if someone is trying to calculate the yield curve of credit spreads. Its better to use zero coupon bonds because cash flows make comparing spread very difficult. If a zero coupon bond is not available an implied zero coupon bond price for the issuer can be derived from the coupon paying bond price.

(1) Use the following spot rate curve to answer this question: Maturity: 1, 2, 3 Spot rates: 5%, 5.5%, 6% The price of a 1-year $1 par, zero-coupon bond to be issued in two years is closest to: A)$0.8396 B)$0.9345 C)$0.9434

Answer B You are trying the forward price of a of a bond issued in 2 years for one year. So N*M of 2 by 3. First you need to find the rate of the forward though. 1.06^3=1.055^2 * (1+FR)^n-m 1.1910=1.113*(1+X)^1 X=.07 Forward Price= Par Value/(1+Forward Rate)^n-m Forward Price= $1/(1.07)^1 FP=.9345

(1) Which of the following choices is least-likely a property of a binomial interest rate tree? A)Non-negative interest rates. B)Mean reversion of interest rates. C)Higher volatility at higher rates.

Answer B A binomial interest rate tree has two desirable properties: non-negative interest rates and higher volatility at higher rates. Binomial trees do not force mean reversion of rates.

(2) On a given day, a bond with a call provision rose in value by 1%. What can be said about the level and volatility of interest rates? A)A possibility is that the level of interest rates remained constant, but the volatility of interest rates rose. B)A possibility is that the level of interest rates remained constant, but the volatility of interest rates fell. C)The only possible explanation is that level of interest rates fell.

Answer B As volatility declines, so will the option value, which means the value of a callable bond will rise.

If a bond has several key rate durations that are negative, it is most likely that the bond is a: A)Putable bond B)Zero coupon bond. C)Callable bond

Answer B Bonds with low (or zero) coupons have negative key rate durations for horizons other than its maturity. This is true for all bonds regardless of whether the bond is callable/putable/straight. Negative Key Rate Duration= When you increase rates, bond value increases. This is true for zero-coupon bonds because if you increase rates any time in-between its maturity, the relationship between par rates, bootstrapping, and spot rates will cause the spot rates to decrease after the rate increase. Since a zero coupon bond has all of its cashflows at maturity, you will now discount those cash flows by a slightly lower rate. This will give you a higher value.

(2) Joseph Dentice, CFA is evaluating three bonds. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. If interest rates decrease, the duration of which bond is most likely to decrease? A)Bond A. B)Bond B. C)Bond C.

Answer B Decrease in rates would increase the likelihood of the call option being exercised and reduce the expected life (and duration) of the callable bond the most. Also as you can see in the pic, the duration (i.e. the change in bonds value/change in interest rates) isn't very much on the callable bond compared to the option free bond.

(1) When Dixon asks about term structure of interest rates, Song mentions that he had attended a seminar on that topic at university the previous semester. While Song could not remember the specific model, he recalled that it had a drift term ensuring mean reversion of rates and a constant level of volatility. The term structure model that Song is referring to is most likely the: A)Cox-Ingersoll-Ross model. B)Vasicek model. C)Ho-Lee model.

Answer B Drift term to ensure mean reversion of interest rates is a feature of the Cox-Ingersoll- Ross model and the Vasicek model. The Cox-Ingersoll-Ross model has volatility increasing with rates (and hence not constant). The Vasicek model assumes constant level of volatility over the period of analysis (i.e., independent of the level of interest rates).

(2) Which of the following is most likely a weakness of reduced form models? A)The model's credit risk changes with the business cycle. B)Hazard rate estimation procedures predict future defaults using historic information. C)The model assumes that a company's equity trades in frictionless markets.

Answer B Note that Reduced form models and Structural models both try to estimate credit risk. Unless the model is properly back tested and formulated, the use of historical data may not be appropriate for predicting the future. Only a single issue of zero coupon debt is assumed to trade under the reduced form models. Under reduced form models, the credit risk is allowed to change with business cycle. This is however, an advantage. There is no requirement that the company's equity is traded. *Assumptions of the reduced form model:* -Company has a zero-coupon bond with a maturity at time T, and it trades in frictionless and arbitrage-free markets. -The risk-free rate, probability of default, and recovery rate are all allowed to vary with the state of the economy. *Strengths of reduced form models*: -Since model inputs are observable, historical estimation procedures can be used. -Credit risk is allowed to fluctuate with the business cycle. -Reduced form models do not require specification of the company's balance sheet structure. *Weaknesses of reduced form models:* Unless the model has been formulated and backtested properly, the hazard rate estimation procedures (using past observations to predict the future) may not be valid.

(1) As she tries to reconstruct what was said at the conference, she writes down two statements about the swap rate curve: Statement 1: The swap rate curve typically has yield quotes at more maturities than government bond markets have. Statement 2: Retail banks are more likely to use the government spot curve as a benchmark as they have minimal exposure to swap markets. Are the two observations Berg records after the fixed income conference accurate? A)Both statements are accurate. B)Only Statement 1 is accurate. C)Only Statement 2 is accurate.

Answer B Statement 1 is correct. Swap markets tend to have more maturities with which to construct a yield curve as compared to government bond markets. Statement 2 is correct. Retail banks tend to have little exposure to swaps and hence are more likely to use the government spot curve as their benchmark. Wholesale banks that manage interest rate risk with swap contracts are more likely to use swap curves to value their assets and liabilities. Retail banks, on the other hand, are more likely to use a government bond yield curve.

(2) Statement 1: The proper spread measure for option-free corporate bonds is the nominal spread. Statement 2: Callable corporate bonds and mortgage-backed securities should be measured using the option-added spread. Statement 3: The Z-spread is appropriate for credit card ABS and auto loan ABS. How many of the three statements on appropriate spread measures and valuation models are correct? A)Only two statements are correct. B)Only one statement is correct. C)None of the three statements are correct.

Answer B Statement 1 is incorrect. The Z-spread is the appropriate spread measure for option-free corporate bonds. Statement 2 is also incorrect, as it should say option-adjusted spread or "option-removed spread." Statement 3 is correct. The Z-spread is the spread that when added to each spot rate on the yield curve makes the present value of a bond's cash flows equal to the bond's market price. The Z refers to zero volatility-a reference to the fact that the Z-spread assumes interest rate volatility is zero. Z-spread is not appropriate to use to value bonds with embedded options. Nominal spread is the difference in YTM between the risky bond and a risk-free bond (usually a Treasury) of the same maturity; it is a spread added to one point on the Treasury par curve. Thus, the nominal spread ignores the term structure of interest rates; it uses only one point, not the entire yield curve. The Z-spread is added to every point on the (zero-volatility) spot curve; it uses the entire yield curve, not just one point. The OAS is added to every point on the (nonzero-volatility) spot curve; it uses the entire yield curve, not just one point. The difference between the Z-spread and the OAS is that the Z-spread includes the spread for any embedded options (along with the spread for all other risks associated with the bond), whereas the OAS removes the spread for the embedded options, leaving only the spread for all other risks associated with the bond. The Z-spread minus the OAS is the price of the empedded option(s), measured in bp of return (instead of being measured in price difference).

(2) The liquidity theory of the term structure of interest rates is a variation of the pure expectations theory that explains why: A)the yield curve usually slopes downward. B)the yield curve usually slopes upward. C)duration is an imprecise measure.

Answer B The pure expectations hypothesis says that the shape of the yield curve only reflects expectations of future short-term rates. Yet, the yield curve generally slopes upward. The liquidity theory says that the yield curve incorporates expectations of short-term rates; however, the tendency for the yield curve to slope upward reflects the demand for a higher return to compensate investors for the extra interest rate risk associated with bonds with longer maturities.

(1) The primary benefit of owning a convertible bond over owning the common stock of a corporation is the: A)bond has lower downside risk. B)conversion premium. C)bond has more upside potential.

Answer B The straight value of the bond forms a floor for the convertible bond's price. This lowers the downside risk. The conversion premium is a disadvantage of owning the convertible bond, and it is the reason the bond has lower upside potential when compared to the stock.

(2) Which of the following is equal to the value of a noncallable / nonputable convertible bond? The value of the corresponding: A)straight bond. B)straight bond plus the value of the call option on the stock. C)callable bond plus the value of the call option on the stock.

Answer B The value of a noncallable/nonputable convertible bond can be expressed as: Option-free convertible bond value = straight value + value of the call option on the stock.

(1) Exhibit 1: Key Rate Durations for Three Fixed-Income Portfolios Key Rate Maturity Portfolio 1 Portfolio 2Portfolio 3 2-year 2.45 0.35 1.26 5-year 0.20 0.40 1.27 10-year 0.15 4.00 1.23 20-year 2.20 0.25 1.24 Total 5.00 5.00 5.00 If the 5- and 10-year key rates increase by 20 basis points, but the 2- and 20-year key rates remain unchanged: A)all three portfolios will experience the same price performance. B)Portfolio 1 will experience the best price performance. C)Portfolio 2 will experience the best price performance. What if If the spot-rate curve experiences a parallel downward shift of 50 basis points:

Answer B and for the second question Each of the portfolios has an effective duration of five, so a parallel shift in the yield curve will have the same effect on each portfolio, and each will experience the same price performance. Key rate duration is the sensitivity of the value of a security (or a bond portfolio) to changes in a single par rate. Key rate duration is defined as the approximate percentage change in the value of a bond portfolio in response to a 100 basis point change in the corresponding key rate, holding all other rates constant. The exposure of each portfolio to changes in the 5- and 10-year rates are equal to the sum of the 5- and 10-year key rate durations: portfolio 1 exposure = 0.20 + 0.15 = 0.35 portfolio 2 exposure = 0.40 + 4.00 = 4.40 %Change in Bond=(-1)(Duration)(increase in % rate)(100). Portfolio 2 has the largest exposure, and portfolio 1 has the smallest exposure. If the 5- and 10-year key rates increase, portfolio 1 will fall by the smallest amount and will experience the best price performance (i.e., the smallest decrease in value). You can confirm this by doing the calculations for a 20 basis point increase: % change in portfolio 1 = (-0.20 × 0.002 × 100) + (-0.15 × 0.002 × 100) = (-0.35 × 0.002 × 100) = -0.07% % change in portfolio 2 = (-0.40 × 0.002 × 100) + (-4.00 × 0.002 × 100) = (-4.40 × 0.002 × 100) = -0.88%

(2) A bond portfolio has the following key rate durations: D2 = 0.50; D5 = 2.70 and D15 = 7.23. Suppose that the change in yield curve results in changes in the following spot rates: S1 = +50bps; S2= +100bps; S5 = +25 bps; S10 = -75bps; S15 = -100bps. The change in the value of the portfolio will be closest to: A)-2.80% B)+4.75% C)+6.06%

Answer C %△P = -(0.50)(1.0)-(2.70)(0.25)-(7.23)(-1) = 6.06%

(2) Suppose that the stock price of a common stock increases by 10%. Which of the following is most accurate for the price of the recently issued convertible bond? The value of the convertible bond will: A)increase by 10%. B)remain unchanged. C)increase by less than 10%.

Answer C Because theres typically a conversion premium (i.e. its not logical to convert until stock price reaches certain price or bond value falls very low) an increase in stock won't correlate to an identical increase in the convertible bond. Vconvertible bond=value of bond + value of convertible option. The minimum value of a bond= Max of straight value or convertible option. The value of the convertible option can be found by finding the convertible value which is the Conversion ratio*$MV of Stock price. As the stock price increases, the option price increases and pushes the value of the convertible bond higher.

(2) Song says that an analyst could use structural models to analyze credit risk of Zena, Inc., bonds, and that one of the ways to evaluate credit risk is to look at the economic exposure of the equity investors. Specifically, owning equity is similar to owning a European option on the assets of the company. While discussing structural models, the European option that Song discusses is most likely a: A)conversion option. B)put option. C)call option. Also what does the structural model say about owning debt?

Answer C Equity investors have call option on assets where debt is the strike price. Thus, if assets are greater than debt then stockholders get the difference (could be in form of dividends). Equity investors can be thought of as holders of a European call option on the assets of the company with a strike price equal to the face value of debt. At the maturity of debt, if the assets of the company are worth more than the face value of debt, the option is exercised (i.e., debt is paid). However, if the assets are insufficient to pay the debt, due to limited liability of shareholders, the option is allowed to expire (i.e., the company defaults).

(2) Which of the following statements regarding settlement protocols with respect to CDS is least accurate? A)When there is a credit event, the swap will be settled in cash or by physical delivery. B)A super majority vote of the declarations committee of ISDA is needed for a credit event to be declared. C)When a credit event has occurred, with physical settlement, the protection seller receives the reference obligation and the protection buyer receives the market value of the reference obligation immediately prior to the credit event.

Answer C In case of physical settlement, the protection buyer receives the notional principal and not the market value of the bond prior to the credit event. When settled in cash the CDS buyer will receive difference between Notional Principal-Market Value. Where market value reflects the credit event. For example a 100 bond with market value of 20 means that creditors expect a recovery value of $20.

(2) NominalSpread OAS Z-spread W 1.21% 0.28% 0.79% X 1.43% 0.49% 1.16% Y 1.62% 0.31% 1.12% Z 1.59% 0.40% 1.14% Of the four MBS securities under consideration, which MBS will add the most value relative to the risk associated with the security assuming the effective durations of the MBS securities is approximately the same? A)MBS-W. B)MBS-Y. C)MBS-X.

Answer C MBS-X has the highest OAS relative to the cost of the option embedded in the MBS. Therefore, it is the most attractive of the four alternatives. As a rule of thumb, a high OAS is good. A high OAS typically means underpriced.

(1) When assessing a company's credit risk using structural models, which of the following statements is most accurate? A)Owning debt is economically equivalent to owning a European call option on the company's assets. B)Owning equity is economically equivalent to owning a risk free bond and simultaneously selling a put option on the assets of the company. C)Structural models do not account for the impact of interest rate risk of the value of a company's assets.

Answer C Owning equity is economically equivalent to owning a European call option on the assets of the company. Owning debt is economically equivalent to owning a risk free bond and simultaneously selling a put option on the assets of the company. The structural model assumes that risk-free rate is not stochastic (i.e., it assumes that risk-free rate is constant). *Assumptions of the structural model:* -Company's assets are traded in a frictionless market with return μ and variance σ2. -The risk-free interest rate (r) is constant. -The company has a simple balance sheet structure. *Strengths of structural models:* Provides option analogy to understand probability of default and loss given default and can be estimated using current market prices. *Weaknesses of structural models:* -Model assumptions of simple balance sheet and traded assets are not realistic. -Estimation procedures do not consider business cycle.

(2) How does the value of a callable bond compare to a noncallable bond? The bond value is: A)higher. B)lower or higher. C)lower.

Answer C Since the issuer has the option to call the bonds before maturity, he is able to call the bonds when their coupon rate is high relative to the market interest rate and obtain cheaper financing through a new bond issue. This, however, is not in the interest of the bond holders who would like to continue receiving the high coupon rates. Therefore, they will only pay a lower price for callable bonds.

(3) Which of the following is NOT a reason why market participants prefer the swap rate curve over a government bond yield curve? The swap market: A)it is not affected by technical factors. B)is free of government regulation. C)reflects sovereign credit risk.

Answer C Swap rate curves are typically determined by dollar denominated borrowing based on LIBOR. These rates are determined by market participants and are not regulated by governments. Swap rate curves are not affected by technical market factors that affect the yields on government bonds. The swap rate curve is also not subject to sovereign credit risk (potential government default on debt) that is unique to each country. Investors use the swap spread to separate the time value portion of a bond's yield from the risk premia for credit and liquidity risk. The higher the swap spread, the higher the compensation for liquidity and credit risk.

(1) Issuer Option-Adjusted Spread AA-rated issuer 53 basis points BB-rated issuer −18 basis points Evermore concludes, based on this information, that the AA-rated issue is undervalued, and the BB-rated issue is overvalued. Is Evermore correct in her analysis of the relative valuation of the bonds? A)Correct on both issues. B)Correct on the AA issue only. C)Correct on the BB issue only.

Answer C The benchmark securities used to create the tree are Treasury securities, so the OAS for each callable corporate bond reflects additional credit risk and liquidity risk relative to the benchmark. The bonds are overvalued if their OAS are smaller than the required OAS and undervalued if their OAS are larger than the required OAS. The required OAS for both bonds is the Z-spread over Treasuries on comparably-rated securities with no embedded options. That required spread is not provided in the vignette. The BB-rated issue is overvalued because its OAS is less than zero, which means it must be less than the required OAS. Therefore, Evermore is correct in her analysis of the BB-rated issue. The AA-rated issue has a positive OAS relative to the Treasury benchmark, but we don't know the required OAS on similar bonds, so we can't determine whether or not the AA-rated issue is over or undervalued based on the information given. Therefore, Evermore is incorrect to conclude that the issue is undervalued.

(1) A putable bond with a 6.4% annual coupon will mature in two years at par value. The current one-year spot rate is 7.6%. For the second year, the yield volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The bond is putable in one year at 99. Using a binomial interest rate tree, what is the current price? A)98.190. B)98.885. C)98.246.

Answer C The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value at all nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices: Vi,U = [(100 + 6.4) / 1.076 + (100+6.4) / 1.076] / 2 = 98.885 Vi,L = [(100 + 6.4) / 1.068 + (100 + 6.4) / 1.068] / 2 = 99.625. Since 98.885 is less than the put price, Vi,U = 99 V0 = [(99 + 6.4) / 1.076) + (99.625 + 6.4) / 1.076)] / 2 = 98.246.

(3) A bond with a 10% annual coupon will mature in two years at par value. The current one-year spot rate is 8.5%. For the second year, the yield volatility model forecasts that the one-year rate will be either 8% or 9%. Using a binomial interest rate tree, what is the current price? A)103.572. B)101.837. C)102.659.

Answer C The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value in nodal period 2: V2=100. In nodal period 1, there will be two possible prices: V1,U=[(100+10)/1.09+(100+10)/1.09]/2= 100.917 V1,L=[(100+10)/1.08+(100+10)/1.08]/2= 101.852 Thus V0=[(100.917+10)/1.085+(101.852+10)/1.085]/2= 102.659

(3) Which of the following statements is most accurate concerning a convertible bond? A convertible bond's value depends: A)only on interest rate changes. B)only on changes in the market price of the stock. C)on both interest rate changes and changes in the market price of the stock.

Answer C The value of convertible bond includes the value of a straight bond plus an option giving the bondholder the right to buy the common stock of the issuer. Hence, interest rates affect the bond value and the underlying stock price affects the option value. Because theres typically a conversion premium (i.e. its not logical to convert until stock price reaches certain price or bond value falls very low) an increase in stock won't correlate to an identical increase in the convertible bond. Vconvertible bond=value of bond + value of convertible option. As the stock price increases, the option price increases and pushes the value of the convertible bond higher.

(1) If the spot curve is upward sloping, the forward curve is most likely to be: A)parallel to the spot curve and below the spot curve. B)parallel to the spot curve and above the spot curve. C)steeper than the spot curve and above the spot curve.

Answer C When the spot curve is upward sloping, the forward curve will be lie above the spot curve and will also be upward sloping with a steeper slope.

(2) In anticipation of an announcement of leveraged buyout of a publicly traded company, which of the following actions would be most appropriate? A)Buy both the stock and the bonds of the company. B)Sell protection of the company's bond and buy put options on the company's stock. C)Buy the stock of the company and buy CDS protection on company's debt.

Answer C In the case of a leveraged buyout (LBO), the firm will issue a great amount of debt in order to repurchase all of the company's publicly traded equity. This additional debt will increase the CDS spread because default is now more likely. An investor who anticipates an LBO might purchase both the stock and CDS protection, both of which will increase in value when the LBO happens.

(1) 7.5%, 15-year, annual pay option-free Xeleon Corp bond trades at a market price of $95.72 per $100 par. The government spot rate curve is flat at 5%. The Z-spread on Xeleon Corp bond is closest to: A)250 bps B)325 bps C)300 bps

Answer C Since the spot rate curve is flat, we can simply compute the yield on the bond and subtract the spot rate from it to obtain the Z-spread. The Z-spread is the spread that when added to each spot rate on the yield curve makes the present value of a bond's cash flows equal to the bond's market price. The Z refers to zero volatility-a reference to the fact that the Z-spread assumes interest rate volatility is zero. Z-spread is not appropriate to use to value bonds with embedded options. PV = - 95.72; N = 15; PMT = 7.50; FV = 100; I/Y=?=8%. Z-spread = 8% - 5% = 3% or 300bps

(2) Compared to a yield curve based on government bonds, swap rate curves are: A)less comparable across countries and have a greater number of yields at various maturities. B)more comparable across countries and have a smaller number of yields at various maturities. C)more comparable across countries and have a greater number of yields at various maturities.

Answer C Swap rate curves are typically determined by dollar denominated borrowing based on LIBOR. These rates are determined by market participants and are not regulated by governments. Swap rate curves are not affected by technical market factors that affect the yields on government bonds. Swap rate curves are also not subject to sovereign credit risk (potential government default on debt) that is unique to government debt in each country. Thus swap rate curves are more comparable across countries because they reflect similar levels of credit risk. There is also a wider variety of maturities available for swap rate curves, relative to a yield curve based on US Treasury securities, which has only four on-the-run maturities of two years or more. Swap rate curves typically have 11 quotes for maturities between 2 and 30 years.

(2) Greg Terry, CFA, suggested to Garret that she utilize the LIBOR swap curve as a benchmark for the Atlantic fund rather than using local government yield curves. Terry justifies his suggestion by claiming that "the lack of government regulation in the swap market makes swap rates and curves directly comparable between different countries despite fewer maturity points with which to construct the curve as compared to a government yield curve. Furthermore, credit risk in the swap curves of various countries is similar, thus avoiding the complications associated with different levels of sovereign risk embedded in government yield curves." Which of the following best evaluates Terry's justification for using the swap curve as the benchmark for the Atlantic Fund? Terry's justification is: A)incorrect because there are different levels of credit risk in the swap curves of different countries. B)correct. C)incorrect because there are actually more maturity points to construct the swap curve.

Answer C Terry's justification is incorrect. There are actually more maturity points in the swap market from which a swap curve can be derived. The rest of Terry's statements are correct.

(2) What are the implications for the shape of the yield curve according to the liquidity theory? The yield curve: A)is always flat. B)must be upward sloping. C)may have any shape.

Answer C The liquidity theory holds that investors demand a premium to compensate them to interest rate exposure and the premium increases with maturity. Even after adding the premium to a steep downward sloping yield curve the result will still be downward sloping.

(2) Suppose the market price of a convertible security is $1,050 and the conversion ratio is 26.64. What is the market conversion price? A)$26.64. B)$1,050.00. C)$39.41.

Answer C The market conversion price is computed as follows: Market conversion price = market price of convertible security/conversion ratio = $1,050/26.64 = $39.41

(3) A convertible bond has a conversion ratio of 12 and a straight value of $1,010. The market value of the bond is $1,055, and the market value of the stock is $75. What is the market conversion price and premium over straight value of the bond? A)$75.00 0.1029 B)$84.17 0.1222 C)$87.92 0.0446

Answer C The market conversion price is: (market price of the bond) / (conversion ratio) = $1,055 / 12 = $87.92. The premium over straight price is: (market price of bond) / (straight value) − 1 = ($1,055 / $1,010) − 1 = 0.0446. Note: Straight value is the value of the bond if it did not have a conversion option. Calculate Premium over Straight Value: this value helps investors interpret downside risk of a convertible bond because the convertible will not trade below its straight bond value. Premium over Straight Value = (Market Price of Convertible / Straight Value) - 1 Minimum Value of a Convertible Bond: a convertible bond should, at the lowest, trade at the higher of either the conversion value or straight value. Conversion Value= Market Price per Common Share*Conversion Ration

(1) Jill Sebelius, editor-in-chief of a monthly interest-rate newsletter uses the following model to forecast short-term interest rates: dr=a(b-r)dt + Std(R^.5)Dz For the current newsletter, Sebelius has issued the following expectations: a=0.40, b = 3%, r = 2%. Sebelius"s model is most accurately described as the: A)Vasicek model. B)Ho-Lee model. C)Cox-Ingersoll-Ross model.

Answer C The model given is an example of the Cox-Ingersoll-Ross model which differs from the Vasicek model by including the square root of current level of short-term interest rates in the stochastic part of the equation. Both the CIR and Vasicek models are Equilibrium term structure models. The Ho Lee model is an arbitrage free model. All of these are modern term structure models.

(1) Evermore also uses the same interest rate tree to price a 2-year 6% coupon bond that is putable in one year, and value the embedded put option. She concludes that if the yield volatility decreases unexpectedly, the value of the putable bond will increase and the value of the embedded put option will also increase, assuming all other inputs are unchanged. She also concludes that the computed OAS for the bond would decrease as the estimated level of yield volatility decreases. Is Evermore correct in her analysis of the effect of a change in yield volatility? A)Incorrect on the puttable bond only. B)Incorrect on the put option only. C)Incorrect on both the bond and the option. Is Evermore correct about the effect of a decrease in estimated level of yield volatility on the computed OAS?

Answer C The value of a putable bond is equal to the value of an otherwise equivalent option-free bond plus the value of the embedded put option. The value of the embedded put option will decrease if yield volatility decreases. The value of the option-free bond will not be affected by changes in yield volatility, so the value of the putable bond will also decrease. Evermore is incorrect in her analysis of both effects. Yes The computed value of a putable bond decreases with a decrease in the assumed level of volatility and therefore the OAS needed to force the model price to be equal to market price will be lower.

(2) Which of the following statements regarding credit ratings is least accurate? A)An advantage of traditional credit ratings is that they provide a simple way of summarizing complex credit analysis. B)A disadvantage of traditional credit ratings is that they are stable over time which reduces the correlation with a debt offering's default probability. C)An advantage of traditional credit ratings is that they tend to vary with the business cycle which accurately reflects current risk.

Answer C Traditional credit ratings tend to be stable over the business cycle. This is a disadvantage as a debt offering's default probability will vary with the cycle. Credit ratings are simple, summary measures of risk that are easy to communicate. However, the ratings do not adjust with business cycle, and the stability in ratings comes at an expense of reduction in correlation with default probabilities.

Carter also manages several active strategies and is evaluating two trade ideas for his portfolios. His forecast, which differs from consensus, is that the economy will weaken and that the yield curve will experience a parallel downward shift. Trade 1: Buy a 10-year AA-rated non-callable corporate bond; Sell a 10-year AA-rated callable bond of the same issuer. Trade 2: Buy a 5-year floating-rate corporate bond; Sell the same issuer's 5-year fixed-rate bond. D. Determine, assuming Carter's forecast is correct, whether he should execute each of the following: i. Trade 1 ii. Trade 2 Justify each response

Answer: Carter should execute Trade 1 given his market outlook. Callable bonds significantly underperform non-callable bonds when interest rates decline because of their negative convexity. Callable bonds do not fully participate in bond market rallies because of the upper bound imposed by call prices. In other words, lower rates mean that the bond is more likely to be called. Therefore, it will be profitable to swap from callable bonds into non-callable bonds when interest rates decline. Carter should not execute Trade 2, given his market outlook. Because he anticipates a parallel downward shift in the yield curve, reducing duration by moving from a 5-year fixed-rate bond to a 5-year floating-rate bond is not appropriate. By investing in the lower duration 5-year floating rate bond, as interest rates declined, it would underperform the higher duration 5-year fixed rate bond.

(2) As the volatility of interest rates increases, the value of a putable bond will: A)rise. B)rise if the interest rate is below the coupon rate, and fall if the interest rate is above the coupon rate. C)decline.

Answer: A As volatility increases, so will the option value, which means the value of a putable bond will rise. Remember that with a putable bond, the investor is long the put option.

(2) FLIP FLIP FLIP Statement 1: Correct. Statement 2: Correct Statement 3: Incorrect. One of the assumptions of the structural model is that default risk is constant during the life of the bond. Be careful, the assumptions is that default risk is constant over life of the bond. the assumption doesn't say default risk is constant over business cycles. Statement 4: Correct: ABS does not default when the underlying collateral defaults. for this reason they use probability of loss of ABS.

Are the following True or False?

(2) FLIP FLIP FLIP If you can sell the bond at $100 in year one then the value at 1U is replaced with $100 and Il is still 103.58 (.5(100+8)+.5(103.58+8))/1.043912)= 105.17

Assume that the bond is putable in one year at par ($100) and that the put will be exercised if the computed value is less than par. What is the value of the putable bond? The value of 1U=99.13 and the value of 1L=103.58 A)$105.17. B)$95.38. C)$103.04.

(2) The OAS most likely reflect: A)simple spreads over the Treasury yield curve. B)average spreads over the Treasury spot rate curve. C)average spreads over the Treasury yield curve.

B. OAS is interpreted as the average spread over the Treasury spot rate curve. The nominal spread is measured relative to the Treasury yield curve. Nominal spread is the difference in YTM between the risky bond and a risk-free bond (usually a Treasury) of the same maturity; it is a spread added to one point on the Treasury par curve. Thus, the nominal spread ignores the term structure of interest rates; it uses only one point, not the entire yield curve. The Z-spread is added to every point on the (zero-volatility) spot curve; it uses the entire yield curve, not just one point. The OAS is added to every point on the (nonzero-volatility) spot curve; it uses the entire yield curve, not just one point. The difference between the Z-spread and the OAS is that the Z-spread includes the spread for any embedded options (along with the spread for all other risks associated with the bond), whereas the OAS removes the spread for the embedded options, leaving only the spread for all other risks associated with the bond. The Z-spread minus the OAS is the price of the empedded option(s), measured in bp of return (instead of being measured in price difference).

FLIP FLIP FLP

Bond 4 is putable because its OAS exceeds its Z-spread. Putable bonds include an embedded long (put) option. The option value and bond price will increase with increasing volatility. Sample Scoring Key: One point for selecting Bond 4. Two points if it is clear you compared the OAS and Z-spread to reach the conclusion Bond 4 will do best with increasing volatility.

(2) When the underlying option is at- or near-the-money, callable bonds will have lower/higher one-sided down-duration than one-sided up-duration. When the underlying option is at- or near-the-money, putable bonds will have lower/higher one-sided down-duration than one-sided up-duration.

Callable bonds will have a lower one-sided down duration because the bonds will get called if rates keep decreasing so the duration loses its sensitivity. Putable bonds will have a higher one sided down duration because the side that will have be affected is the up duration. The duration will lose sensitivity as rates increase because you can exercise the put.

(3) FLIP FLIP FLIP (.5(98.565+8)+.5(99.455+8))/1.079629=99.13 for 1U (.5(99.455+8)+.5(102.755+8))/1.053310= 103.58 for 1L (.5(103.58+8)+.5(99.13+8))/1.043912=104.76 for 0

Compute V0, the value of the bond at node 0. A)$104.76. B)$101.35. C)$99.07.

(2) Convexity for straight bonds is neg/pos Convexity for callable bonds is neg/pos for near the money/out of money Convexity for putable bonds is neg/pos

Convexity is positive when the impact of a rate decrease on bond prices is higher than the impact of a rate increase. -Convexity for straight bonds is pos -Convexity for callable bonds is neg for near the money. -Convexity for putable bonds is always pos

Key Rate Duration 2 year: 0.50 5 year: 1.20 15 year :0.80 If Short term rates change by 70bps, medium term change by 0, and long term change by 80 What is the effective duration?

Durations are always negative to start with. They essentially tell you the percentage that your bond price will be effected by interest rates increase by 100basis points.

(3) Regarding Reduced Form Models, True or False -It must be assumed that the risk less rate of interest is constant over time. -For a given state of the economy, whether a company defaults depends only on company specific considerations -The time T value of the company's assets has a lognormal distribution -Both structural and reduced form assume that assets trade in frictionless market

F, T, F,F Structural models assume that the risk free rate is constant and that the company's assets trade in frictionless market and they have a lognormal distribution. Reduced form models assumes that the company has one zero coupon debt that trades in frictionless market. It does not assume its assets trade. Reduced form models have a vector for the variables that are not constant that represents macroeconomic factors such as a boom period, recession, depression. This is why the model captures changing economic conditions. Once an economic condition is chosen then a companies default depends on the company's own actions or company specific risk For example: In a recession Ford's probability of default will increase as the macroeconomic factors captured in the model move unfavorably. This represents systemic risk. Whether Ford actually defaults given the recession, depends on the company's specific risk.

How do you immunize a liability? What are the two rules?

First the portfolio must match the duration of the liability. Second, the initial present value of all cash flows must equal the present value of the future liability

(2) How does higher volatility impact OAS for a callable bond? how about for a bond with put option?

Higher volatility for a callable bond decreases OAS. Higher Volatility for bond with put option increases OAS. In the pic, higher volatility for call option, increases value of call option to the issuer. This decreases the bond price to the buyer. However this lower bond price will still be higher than market price because to calculate bond prices with embedded options you use binomial interest rate trees (which discount at risk free rate i.e. too low discount rate causes high prices) Nonetheless, with a lower starting off price (due to high value of call option), the OAS will ultimately be lower. Hence, the spread that you add to the risk free rate in the interest rate tree will be lower. With a putable bond, volatility increases put. This increases your bond price. This makes your OAS have to be higher in order to match the market rate. I.E. your gonna have to discount by a greater amount.

If one expects that the future spot rate will be lower than what is predicted by the prevailing forward rate, the forward contract value is expected to increase/decrease.

Increase. To capitalize on this expectation the trader would buy the forward contract.

(2) What is an OAS? (option adjusted spread?) What is implied when the Z spread is higher than OAS? What about when the Z spread is lower than the OAS?

It's basically the Z-Spread but for the rates used in binomial interest rate trees. The rates used are for benchmark treasury securities, so you need to bump them up in order to fully compensate for a company bond since a corporate bond will have a risk premium and liquidity premium above the treasury rates. If Z-Spread higher than OAS then this implies that bond has a call option to the issuer. Meaning theres less value to the buyer than what the Z Spread implies. Note that the Z Spread lacks the ability to price in option values. If Z-Spread is lower than the OAS then this implies that the bond has a put option to the buyer. Meaning theres more value to the buyer that is picked up by the OAS.

(1) What is key rate duration and which time period change will cause the biggest duration change for a straight bond? how about for a callable bond and putable bond out of the money? what if they are in the money?

Key rate duration is the duration if you change the rate on a specific spot rate instead of changing all rates simultaneously (which implies a linear shift to interest rates). For a straight bond or deep out of the money callable bond or putable bond, the rate at maturity will cause the most changes. Since this is when you receive the largest cash flow and you will discount this amount by the most periods using the new rate. For a callable/putable bond that is near the money the rate at the call/put date will cause the most changes to duration.

What is difference between Z Spread, Nominal Spread, and OAS spread?

Nominal spread is the difference in YTM between the risky bond and a risk-free bond (usually a Treasury) of the same maturity; it is a spread added to one point on the Treasury par curve. Thus, the nominal spread ignores the term structure of interest rates; it uses only one point, not the entire yield curve. The Z-spread is added to every point on the (zero-volatility) spot curve; it uses the entire yield curve, not just one point. The OAS is added to every point on the (nonzero-volatility) spot curve; it uses the entire yield curve, not just one point. The difference between the Z-spread and the OAS is that the Z-spread includes the spread for any embedded options (along with the spread for all other risks associated with the bond), whereas the OAS removes the spread for the embedded options, leaving only the spread for all other risks associated with the bond. The Z-spread minus the OAS is the price of the empedded option(s), measured in bp of return (instead of being measured in price difference).

(1) Describe the option analogy of the structural model

Owning stock of a company with debt is the same as owning a call option on the company's assets with the strike price being the company's debt. Thus when your assets are above the company's debt, the shareholders are entitled to the residual. The value of risky debt: Value of Debt+ short put on asset assets with strike price being debt. Or value of debt-put option on assets with strike price being debt. The short put is betting that the company assets will be above the strike price. The strike price is the company's debt. If this isn't the case then assets are below debt and you subtract this from the original value of debt. If volatility increases, this increases the value of the short put and thus will decrease the value of your risky debt. Thus under the structural model option analogy your bond or debt would decrease in value.

(2) When an analyst uses a lower-than-actual level of volatility, the computed OAS for a callable bond will be too high/low and the callable bond will be erroneously classified as underpriced/overpriced Similarly, when the analyst uses a lower-than-actual level of volatility, the computed OAS for a putable bond will be too low/high and the putable bond will be erroneously classified as overpriced/underpriced

Remember Value of Callable bond= Value of straight bond- value of call When analyst uses too low volatility the value of call will be too low which makes value of bond too high. The OAS additional discount to get to market price will be too high. This will make callable bond incorrectly underpriced. Remember Value of Put Bond= Value of Straight bond + Value of Put When analyst uses too low volatility the value of put will be too low which makes value of bond too low. The OAS additional discount to get to market price will be too low (since the bond is already priced pretty low without the OAS spread). This will make putable bond incorrectly overpriced.

In sum, find the current dollar duration. Then wanted duration-current dollar duration/current= rebalancing ratio rebalancing ratio*current market value=amount of cash needed. Answer C (Dollar Duration)P, in one year = DDP, in one year = ((9.46 * 10,000,000 * (104.98/100)) + (7.83 * 25,000,000 * (98.36/100)) + (6.51 * 15,000,000 * (101.21/100)))*(0.01) = ((9.46 * 10000000 * (104.98/100)) + (7.83 * 25000000 * (98.36/100)) + (6.51 * 15000000 * (101.21/100)))*(0.01) = 3,906,823.45 (Rebalancing Ratio) = DDP, today/DDP, in one year = $4,901,106-$3,906,823.45 / $3,906,823.45 = .2545 We must increase the value of the portfolio by the rebalancing ratio, which assumes a proportionate increase in each bond. To do this, multiply the necessary percentage increase by the total value of the portfolio. (Required Cash) = ((Rebalancing Ratio)-1)*(Total value of the portfolio) = ((.2545)-1)*((10,000,000 * (104.98/100)) + (25,000,000 * (98.36/100)) + (15,000,000 * (101.21/100))) = ((.2545)-1)*((10000000 * (104.98/100)) + (25000000 * (98.36/100)) + (15000000 * (101.21/100))) = 12,793,587.75

Suppose that the original dollar duration of the portfolio was $4,901,106 and that the bond prices remain constant during the year. Based on the durations one year from today, and assuming a proportionate investment in each of the three bonds, the amount of cash that will need to be invested to restore the average dollar duration to the original level is closest to: A. $5,885,167. B. $10,888,662. C. $12,793,588.

(2) When would an OAS be higher or lower than the Z Spread?

The OAS is basically the Z-Spread but for the rates used in binomial interest rate trees. The rates used are for benchmark treasury securities, so you need to bump them up in order to fully compensate for a company bond since a corporate bond will have a risk premium and liquidity premium above the treasury rates Z-Spread higher than OAS then this implies that bond has a call option to the issuer. Meaning theres less value to the buyer than what the Z Spread implies. Note that the Z Spread lacks the ability to price in option values. If Z-Spread is lower than the OAS then this implies that the bond has a put option to the buyer. Meaning theres more value to the buyer that is picked up by the OAS.

(1) FLIP FLIP FLIP Expected Loss= % probability of default*Loss given default. Or PV or Riskfree-PV or risky bond Tip: e^Rate*(1/#compound periods per year) 25/e^.0023*.5=24.97 1025/e^.0025(1)=1022.44 PV of risk free=1047.41 25/e^.0103*.5=24.87 1025/e^.011(1)=1013.79 PV of risk free=1038.66 1047.41-1038.66=8.75 An example of the present value with continuous compounding formula would be an individual who in two years would like to have $1100 in an interest account that is providing an 8% continuously compounded return. To solve for the current amount needed in the account to achieve this balance in two years, the variables are $1,100 is FV, 8% is r, and 2 years is t. The equation for this example would be PV@0= Cash flow@t/e^r(t) where R is just your yearly rate. and T is the time you are discounting. For half year: T=.5 For full year: T=1 If discounting two years: T=2

The present value of the expected loss of zeta bond is? A)$7.74 B) $8.25 C) $8.76

(3) If volatility rises how will this effect the price of your callable bond? or bond with a put option?

The value of the callable bond decreases if the interest rate volatility inreases because the value of the embedded call option increases. Since the value of the callable bond is the difference between the value of the non-callable bond and the value of the embedded call option, its value has to decrease. In other words, volatility increases the value of the call option which decreases the value of the call bond. A put option increases with volatility. The value of bond with put options= value of bond + put option. Therefore, value of bond with put option increases when volatility increases.

(1) False/True "Rolling down the yield curve" is an active bond portfolio management strategy that involves buying bonds with maturities longer than our investment horizon. This strategy is profitable only when the yield curve is downward sloping. Active bond portfolio management entails comparing our expected future spot rates to current forward rates. If our expected future spot rate applicable for a bond is greater than the corresponding current forward rate, we would consider that bond to be overvalued.

True/False Rolling down the yield curve is an active strategy. As the time to maturity lessens your discount rate becomes lower but your bond is still paying the same coupon rate which is why theres a gain but only if the yield curve is upward sloping. If an investor's expected future spot rates are higher than the current forward rates for the same maturity, the investor would consider the bond to be overvalued. This is so because the market is discounting the future cash flows at too low a discount rate compared to investor expectations, leading to too high a valuation for the bond. The second statement is True. If you think rates are going to be higher than the what the market thinks, then the bond market is overvalued. As rates rise prices fall.

(1) Flip Flip Flip (91.73+3+96.17+3)/2=96.95/(1+ .0791/2) thus 96.95/1.0395=93.26% Don't get confused by there percentages they basically mean the % of par. Thus 91.73% means 91.73% of Par. If par is 100 then the value at that node is 91.73.

You have a semi annual non callable bond with a coupon rate of 6%. What is the price of the bond using the picture? A) 89.84% B)93.26% C)96.14%

What is key rate duration and why is it important to try to match key rates when doing liability matching?

You only need to know the sensitivity to interest rate changes at certain important points on the yield curve, such at the 3-month rate, 6-month rate, 1-year rate, 2-year rate, 5-year rate, etc. And each of these individual durations is called a "Key Rate Duration"... Now you're getting somewhere. Why would I want to match a benchmark's key rate durations? To hedge your portfolio against twists (non-parallel) shifts in the yield curve.